The title claim is not surprising. But it occurs to me that it follows from how I model prices of production, given stable relative profit rates among industries. I am not original with this modeling. My contribution is analying the choice of technique and exploring how this analysis varies with perturbations of relative markups.
In the price equations, s1 r, s2 r, s3 r, and so on are the rate of profits in the various industries. I call r the scale factor for the rate of profits. Given the technique and a given wage in terms of a given numeraire, one can find prices and the scale factor for the rate of profits. The scale factor is a declining function of the wage. The cost-minimizing technique at a given wage is the technique for the wage curve on the outer frontier at that wage. At a switch point, more than one technique is cost-minimizing.
In the case of competitive markets, 1 = s1 = s2 = s3 = ... The analysis of the choice of technique reduces to the usual analysis in the literature.
The cost-minimizing technique, at a given wage, varies, in general, between the competitive case and the case with with relative markups varying among industries. The cost-minimizing technique is efficient, in some sense, in the competitive case. The outer frontier is sometimes called the efficiency frontier. (I could stand to review what efficiency means in this case.)
Anyways, the above outlines an argument for the title claim based on the analysis of the choice of technique in models of the production of commodities by means of commodities.
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